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In a Wheatstone’s bridge all the four arms have equal resistance R. If the resistance of the galvanometer arm is also R, the equivalent resistance of the combination as seen by the battery is

1. 2R
2. R / 4
3. R / 2
4. R

Correct answer: R / 2

Solution

In a balanced Wheatstone bridge with all arms having equal resistance R, the galvanometer branch does not affect the circuit. The equivalent resistance of the two parallel branches, each having two resistances in series (R + R = 2R), is (2R || 2R) = R. Adding the galvanometer resistance R in series gives the total equivalent resistance as R/2.

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